Assessing elevated pressure impact on photoelectrochemical water splitting via multiphysics modeling

Photoelectrochemical (PEC) water splitting is a promising approach for sustainable hydrogen production. Previous studies have focused on devices operated at atmospheric pressure, although most applications require hydrogen delivered at elevated pressure. Here, we address this critical gap by investigating the implications of operating PEC water splitting directly at elevated pressure. We evaluate the benefits and penalties associated with elevated pressure operation by developing a multiphysics model that incorporates empirical data and direct experimental observations. Our analysis reveals that the operating pressure influences bubble characteristics, product gas crossover, bubble-induced optical losses, and concentration overpotential, which are crucial for the overall device performance. We identify an optimum pressure range of 6–8 bar for minimizing losses and achieving efficient PEC water splitting. This finding provides valuable insights for the design and practical implementation of PEC water splitting devices, and the approach can be extended to other gas-producing (photo)electrochemical systems. Overall, our study demonstrates the importance of elevated pressure in PEC water splitting, enhancing the efficiency and applicability of green hydrogen generation.

by taking into account the pressure difference due to surface tension between the spherical bubble surface (i.e., the Laplace pressure) and the vapor pressure of water.where  loc denotes the local current density,  el is the surface area of the electrode,  e and  are the electron stoichiometry in the reaction and the Faraday constant, respectively.
Finally, the O2 bubble formation efficiency can be calculated by taking the ratio of ̇O 2 and ̇O 2 ,theory .pressure agree relatively well with the measured values.We briefly note that measurement at certain locations were not possible since bubbles located at the background blocked the view.This is especially the case at the top of the electrode, where electrical contacts were made.The contact was done by fixing a copper wire on the electrodes, which was then covered with silicon glue.
Bubbles were likely to be accumulated in these regions during our experiments, as can be seen from the shadows at the top of Supplementary videos S1-S4.
We also validated our model by comparing the dissolved gas concentration to that obtained from the empirical relationship reported by Shibata and Vogt. 4,5As shown in Fig. S6, both the dissolved O2 and H2 concentrations obtained from our model are much higher than the solubility values, and they are in relatively good agreement with the empirical supersaturated concentration; slight deviation can be explained by the fact that no bubble formation is considered in the empirical correlation. w is the predicted concentration of O2 or H2 in the vicinity of electrode based on the empirical equation in literature. 4,5 s is the molar solubility of gas in water, which is calculated based on Henry's law:  s =  g  H ⁄ , in which  g is the partial pressure of the products.Henry's constants for oxygen and hydrogen are  H,O2 = 769.2atm M −1 and  H,H2 = 1282.05atm M −1 , respectively, 6,7 assuming that the solution is pure water and the temperature is 298 K.
O 2 ,our model and  H 2 ,our model are the simulated O2 and H2 concentrations using our model, respectively.j is the current density, which is 10 mA cm -2 in this case.(see Fig. S9).Finally, the bubble-induced optical loss ( opt.loss ) is therefore given by the following:

Figure S1 .
Figure S1.(a) Photographs and (b) schematic illustration of the experimental setup for bubble

Figure S3 .
Figure S3.(a) Schematic illustration of a membrane-free PEC water-splitting device and the

Figure S6 .
Figure S6.Supersaturated concentration of (a) O2 and (b) H2 gases in the vicinity of electrodes.

Figure S7 .
Figure S7.Molar flux of O2 (black) and H2 (red) at the device outlet from the convective (solid)

Figure S9 .
Figure S9.Transmittance measured through a transparent (photo)electrochemical cell at 1 bar

Table S1 .
The coefficients for the generic fitting equation (equation 1) of  O 2 ,  H 2 ,  O 2 and  H 2 .

Table S2 .
Variables considered in our model.